I've been watching your post - and think that you might just have a bigger problem - that of a cracked block. Flatheads with the siamesed exhaust where the two center cylinders have a single block port have ancient a history of cracking if you overheat. The fact that you are continually having to add water is often an indicator. What happens - the overheat condition, and it might only take once for it to happen - is that the exhaust valve seat will crack. This crack can go a couple of different directions, but the most common is into the cylinder wall. Here are some photos of cracks:: http://http://flatheaddrag.com/cracks.html

These cracks can be fixed, but that Chevy belly button engine price starts to look good about that time.

Pull the head on the side that wiped out the temp sender and take a look - it only takes an hour or so, off and then back on (and I've even been known to reuse those head gaskets, especially if it was a copper one)

Flatheads are great nostalgia engines - unfortunately, have gotten way too expensive for parts as well as trying to find anyone that knows much about them